An ideal gas is taken from an initial state i to a final state f in such a way that the ratio of the pressure to the absolute temperature remains constant. What will be the work done by gas?

Question

Philoid · Accepted Answer

Given

Initial pressure P_i

Final pressure P_f

Initial temperature T_i

Final temperature T_f

It is given that

From ideal gas equation, we know

PV=nRT

Where V=volume of gas

R=gas constant

n= number of moles

applying ideal gas equation for both processes, we get

And

From equation (i), (ii) and (iii), we get

∴ V_i=V_f

We know that,

Work done = force ×displacement

Volume = area ×displacement

Therefore,

Work done=pressure × volume

Let change in the volume of system = ΔV = V_f-V_i

Pressure =P

Thus, work done by the gas

ΔW=PΔV=P (V_f-V_i) =0

∴ work done by the gas is zero.